The invention relates to a method for determining the solvent accessible surface area of a molecule with respect to atomic coordinates, wherein the molecule comprises a plurality of atoms, each atom is represented by a sphere having a radius and a center position, and the solvent accessible surface area of the molecule is determined depending on the sum of the solvent accessible surface areas of its atoms.
The method also relates to a system for determining the derivatives of the solvent accessible surface area of a molecule with respect to atomic coordinates, wherein the molecule comprises a plurality of atoms, each atom is represented by a sphere having a radius and a center position, and the system comprises means for determining the derivatives of the solvent accessible surface area of atoms depending on the radius and center position of the spheres.
The invention further relates to a processor in a system for performing a molecular dynamics simulation for a system of molecules comprised of atoms and to a computer program for the molecular dynamic simulations based on determining the solvent accessible surface area of atoms and its derivatives, wherein the computer program is executable on a processor in a system for performing a molecular dynamics simulation.
In order to determine the positions, velocities, and energies of the particles, e.g. the atoms, in the simulations over a period of time, knowledge about the forces between the particles is required. For determining the energy and other thermodynamic properties of the system, the solvent accessible surface of each atom is required. For determining the forces acting on each atom, derivatives of the solvent accessible surface of each atom are required. Techniques known as molecular dynamics determine the positions, velocities and properties of the particles by simulating the physical process in a computer model and thus give insight into all properties of the system and the interaction of the molecules with high temporal and spatial resolution. Molecular dynamics is frequently used in the study of proteins and other biomolecules, as well as in materials science. Molecular dynamics is a technique to perform virtual experiments that increasingly replaces the need to perform costly experiments in the laboratory. Molecular dynamics simulations also permit the study of processes not readily observable with present day experimental techniques (because of the small size of the system, the speed of the process or both).
One kind of molecules are proteins, which perform the vast majority of all biological processes in all cells of plants, animals or humans. The function of these biological macromolecules is regulated in a biological system by binding small molecules (ligands) to the proteins or by the interaction of proteins with other proteins or by the interaction of proteins with DNA. When the function of a certain protein is involved in a certain disease, it is possible to interfere with its function using artificial ligands, which are the most common mechanism of drugs in use today. Since the structure of many (>40.000) disease-relevant proteins is known, in-silico design of new drugs is possible by performing molecular dynamics simulations that simulate the process of binding of the small molecule to the protein in question. In order to influence the function of a protein, a drug has to bind better to the protein than the natural ligand. Currently, molecular dynamics is the most accurate method to determine the binding-strength of both the natural ligand and the proposed molecules.
Furthermore, if a drug has known side effects, it is possible to link the drug molecules with the target molecules so that the drug works mostly in the affected cells, for instance, in a cell affected by cancer. Molecular dynamics can be used to determine how such drug-target complexes bind to the target protein of the drug and how the drugs enter the cell through the membrane.
Molecular dynamics are also used in order to determine the function of a protein, aspects of its structure, the interaction between proteins, and the interaction of proteins and other molecules, such as DNA or man-made molecules emerging from research in the nano sciences.
In the field of materials sciences, molecular dynamics are used to determine material properties, for example the structure and function of organic light emitting diodes, the efficiency of lithium-ion batteries, or the structure and function of nano materials, e.g. single atom transistor or carbon nanotube sorting.
Summarized, molecular dynamics is a method to replace experiments in the laboratory in many fields of science and to permit analysis of the time-dependent behaviour of a molecular system. This knowledge is used to investigate the structure, dynamics, and thermodynamics of biological molecules, their complexes and systems relevant for materials research.
In order to obtain accurate results in molecular dynamics simulations the system must be modelled in its experimentally relevant environment, which is particularly important for systems in solution. One possibility to perform such simulations is to include a large number of solvent molecules explicitly in the simulation, which is performed in a finite simulation volume. In order to avoid edge effects at surface of this volume, periodic boundary conditions are required in such simulations. In a simulation with periodic boundary conditions the system is mathematically replicated periodically in each space direction, such that the particle leaving the simulation volume at the left automatically re-enters it from the right. Periodic boundary conditions permit simulation of an infinite systems, which has no boundaries and therefore no edge effects.
An alternative to this approach are implicit solvent models, which compute forces and properties of the molecular system excluding the solvent by introducing effective energy contributions/forces acting on the atoms of the system. The use of implicit solvent models significantly reduces the number of atoms that have to be simulated and thereby the number of instructions a processor must perform to simulate the system. Use of implicit solvent models also avoids the use of periodic boundary conditions, which simplifies significantly the computation of particular energy contributions, such as electrostatic interactions, which occur in almost all molecular systems.
Performing molecular dynamics simulations has limitations in size and time scale due to the available computing resources. Therefore, molecular dynamics simulations of the required complexity cannot be executed on standard processors, because the processing power of such standard processors is too low. This led to the development of special processors and/or architectures in order to substitute or support standard (main-)processors while performing molecular dynamics simulations. Such special processors and/or architectures include the Cell processor (IBM/SONY), graphics processing units (GPUs) (ATI/NVIDIA), and FPGA (Field Programmable Gate Array) processors, which can be integrated into standard PC-type computers.
Currently, state-of-the-art GPUs can perform over 500 billion arithmetic operations per second. According to recent advances in GPU hardware and software architecture, such processing units can now be utilized for general purpose computing and in particular for molecular dynamics simulations. Although these special processors and architectures are—at least theoretically—up to 1000 times faster than standard processors known from personal computers, this hypothetical gain cannot be realized in simulating molecular dynamics using periodic boundary conditions, because of technical reasons, e.g. the high number of inter-processor communications and the high number of processor-memory communications that are needed to evaluate certain mathematical expressions when using periodic boundary conditions.
Such simulations can be performed much faster using special processors when using implicit solvent models. Most implicit solvent models require the computation of the solvent accessible surface and its derivatives for each atom of the molecule at each time-step of the simulation. Typical simulations performed today comprise 100-100.000.000 atoms for which forces must be computed in 106-1012 simulation steps, resulting in the need to compute up to 1020 derivatives of the solvent accessible surface area in one simulation. The determination of the derivatives of the solvent accessible surface area significantly contributes to the total computing complexity of the molecular dynamics simulation, because to date an exact expression for the computation of the derivatives of the solvent accessible surface area is not available. Using established approximate methods for the computation of the derivatives of the solvent accessible surface area requires 10.000-100.000 computer operations for each atom and time-step (depending on the accuracy of the approximation). Using approximate methods to compute the derivatives of the solvent accessible surface thus induces a high cost of computation and reduces its accuracy, because the use of approximate methods results in errors in the computation of the forces and the computed properties of the system
It is therefore an object of the present invention to provide an exact method and system for determining the derivatives of the solvent accessible surface area of a molecule that can be used e.g. in molecular dynamics simulations and enable to perform these simulations significantly faster and more accurate than currently known methods.